Applicants also would be able to track the progress of their applications and see where they are on waiting lists to rent units, which are awarded by lottery. By 2021, residents also would be able to verify with the city that they are being charged a legal rent.

The legislation is meant to make the application and search process more transparent and efficient, said the bill’s lead sponsor, Council Member Benjamin Kallos.

“I want to make it more like StreetEasy or Zillow,” Mr. Kallos said, referring to the popular housing search websites.

The city already runs a website that helps tenants find income-restricted apartments, NYC Housing Connect, but Mr. Kallos said it is “incredibly broken” because it doesn’t do enough to match tenants with available units.

Since the 1990s, New York City has published, and public officials have quoted, an estimate that there are 1 million rent-stabilized apartments in the city, giving some 2 million tenants protections from eviction and unlimited rent increases.

The estimate comes from the city’s Department of Housing Preservation and Development, or HPD, which publishes a survey on which the number is based. Rent-stabilized apartments are vital to affordable housing and thus an important gauge of the housing market.

There’s one problem with the figure, however: It could be off by as much as 20 percent.

Data provided to ProPublica by the state’s Division of Housing and Community Renewal (DHCR) — which oversees rent-stabilized apartments — shows that, as of 2014, New York City had 839,797 rent-stabilized apartments registered with the state. For that same year, HPD’s survey estimated 1,029,918 units.

Last month, Werner met with City Council Member Ben Kallos to discuss enforcement and administration of the law, which is shared by HPD, the city’s Department of Finance and the state Division of Housing and Community Renewal (DHCR). A reporter also attended.

“We have a bureaucratic quagmire between DHCR, HPD and DOF and we as a city and a state must get to the bottom of it,” Kallos said at the meeting. He called Werner “a hero” for raising the issue.